where \(h(\mu _{A_i})\)  denotes the binary entropy functionFor any \(p \le 1\)  we have: \(h(p) = p \log _2 p + (1-p) \log _2(1-p)\) . and where the last equality derives from the observation that for a binary random variable \(A\) , \(\mu _A = P_A(1)\) . We also observe that equality holds if and only if the random variables \(A_i\) 's are independent. To maximize the rightmost term in equation (REF ) subject to \(\sum _i \mu _{A_i} = n \alpha \) , we observe that the binary entropy is a concave function [1]}, and hence the maximum of the sum is obtained when all \(\mu _{A_i}\) 's are equal, that is when \(\mu _{A_i} = \alpha \) .
